The Irish premier has indicated he backs the idea of charging the UK to leave the EU - a bill that many believe would be about £50bn.
As the PM meets EU leaders for the last time before Article 50 is triggered, Ireland's Enda Kenny told Sky News Political Editor Faisal Islam: "When you sign on for a contract you commit yourself to participation. And obviously the extent of that level of money will be determined."
Mr Kenny, who made the comments as he arrived at the EU Council meeting in Brussels, said the bloc's chief Brexit negotiator, Michel Barnier, would lead any such negotiations.
"Britain will have a say," added Mr Kenny.
"But that... will have to be faced, it will have to be dealt with and it will be dealt with."
Mrs May did not directly address the prospect of a massive bill to settle EU budget commitments, but said: "When people voted on 23 June for us to leave the European Union, they voted for us in the future not paying huge sums of money into the European Union every year.
"And of course when we leave the EU that will be the case."
Of the mooted £50bn figure, Italian Europe minister Sandro Gozi told Sky News: "I think it is going to be around the figure."
Brexit negotiator Mr Barnier refused to comment as his arrived in Brussels, but later said he had agreed a "common position" on the Brexit budget with Bulgarian president Rumen Radev.
Mr Radev will hold the EU presidency in the first half of next year - likely to be a crucial period in Brexit talks.
Former work and pensions secretary Iain Duncan Smith told Sky's Adam Boulton he did not accept a 'divorce bill' was inevitable.
"Legally, we don't have any obligation to pay a damn thing," said the Tory MP.
"It's about the negotiations: as the Germans have said, you can't expect the British to accept that they owe any money if they don't know what the arrangements are afterwards.
"You have to have all of that in the negotiations at the same time."
Mrs May has said she will formally kick off Brexit negotiations by the end of month by invoking Article 50, but legislation on the issue has been held up by two Lords' defeats.
Once the PM has given notice, the clock will start ticking on a two-year period to negotiate a deal.
Meanwhile, as EU leaders gather in the Belgian capital, they have also confirmed Donald Tusk will get another term as Council president.
The Polish politician faced attempts from the prime minister of his home country to block him, but will now continue to play a central role in hammering out a Brexit deal.